Quantum algorithms for condensed-matter physics, number theory and quantum machine learning
Title (trans.)
Algoritmos cuánticos para física de la materia condensada, teoría de números y aprendizaje de máquina cuánticaAuthor
García Martín, DiegoEntity
UAM. Departamento de Física TeóricaDate
2022-11-21Subjects
Hamilton, Sistemas de-Aplicaciones científicas; Números algebraicos, Teoría de los-Aplicaciones científicas; Materia condensada; FísicaNote
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de Lectura: 21-11-2022Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
Quantum computing is a novel paradigm that seeks to harness quantum mechanical
e ects like superposition, entanglement and interference to outperform
classical computers based upon bits (i.e. zeroes and ones) on certain tasks.
Research into the eld of quantum algorithms has produced some exponential
speed-ups over the best classical algorithms currently known, with potential
applications far beyond the academic domain. Yet, the quest for quantum algorithms
that dramatically outperform their classical counterparts has proved
to be hard. New quantum algorithms are needed, together with a better understanding
of the type of problems quantum computers excel at.
In this thesis, we explore the capabilities that quantum computers may o er
to Condensed-Matter Physics, Number Theory and Quantum Machine Learning.
We do so by introducing novel quantum algorithms, both exact and variational,
in Chapters 2, 3 and 5. Moreover, we provide in Chapter 4 the rst
theoretical study of the so-called overparametrization phenomenon in variational
quantum circuits, which is likely to play a relevant role in Quantum Machine
Learning. In Chapter 6, we analyze the scalability of certain Hamiltonian learning
quantum algorithms that rely on Bayesian inference to a large number of
qubits.
Chapter 2 also contains original contributions to Quantum Number Theory,
a novel approach to Number Theory that employs the tools provided by the
formalism of Quantum Information Theory to study mathematical objects like
the prime numbers. Finally, in Appendix A we introduce qibo, an open-source,
high-performance library for the classical simulation of quantum circuits, that
has been used in most of the works presented in this thesis
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